Interferometers are commonly used to measure surface topographies of optical elements. A propagating light wave of constant phase is divided into two wavefronts that are directed along separate optical paths, namely, a test path and a reference path. The test path includes the optical surface being tested, and the reference path includes a known reference surface. After reflecting from test and reference surfaces, the two wavefronts are recombined forming an interferogram. Fringe patterns of the interferogram are interpreted to obtain measures of the surface topography of the test surface.
A majority of precision optical surfaces are spherical segments. The known interferometric techniques are especially well suited to measure concave spherical surfaces. For example, a point light source may be located in the test path at the center of curvature of the concave test surface. To the extent that the test surface is truly spherical, the light impinges at normal incidence to the test surface and is retroreflected along its original path back to the light source. Any deviation of the reflected light from its original path produces fringe distortions in an interference pattern with a reference wavefront indicative of a departure from sphericity.
However, it is much more difficult to use interferometric techniques to measure large convex spherical surfaces. Additional optical elements are used to relay an image of the point source to the center of curvature of convex surfaces. The point source image is relayed by lenses that must be made large enough to produce a converging light beam having marginal rays at normal incidence to the periphery of the convex surface. These lenses are expensive and difficult to make to required accuracy. In fact, it becomes impractical to manufacture optical elements with sufficient accuracy for measuring certain large aperture convex surfaces with the known interferometric techniques.